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Short Proofs of Tverberg-Type Theorems for Cell Complexes.

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Title: Short Proofs of Tverberg-Type Theorems for Cell Complexes.
Authors: Karasev, Roman1 (AUTHOR) remove@gmail.com, Skopenkov, Arkadiy2 (AUTHOR) skopenko@mccme.ru
Source: Discrete & Computational Geometry. Jul2026, Vol. 76 Issue 1, p534-538. 5p.
Subjects: Topology, Continuous functions, Topological spaces, Topological property
Abstract: We present short proofs of Tverberg-type theorems for cell complexes by S. Hasui, D. Kishimoto, M. Takeda, and M. Tsutaya. One of them states that for any prime power r, any complex X topologically homeomorphic to S (d + 1) (r - 1) - 1 , and any continuous map f : X → R d there are pairwise disjoint faces σ 1 , ... , σ r of X such that f (σ 1) ∩ ... ∩ f (σ r) ≠ ∅ . [ABSTRACT FROM AUTHOR]
Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Short Proofs of Tverberg-Type Theorems for Cell Complexes.
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  Data: We present short proofs of Tverberg-type theorems for cell complexes by S. Hasui, D. Kishimoto, M. Takeda, and M. Tsutaya. One of them states that for any prime power r, any complex X topologically homeomorphic to S (d + 1) (r - 1) - 1 , and any continuous map f : X → R d there are pairwise disjoint faces σ 1 , ... , σ r of X such that f (σ 1) ∩ ... ∩ f (σ r) ≠ ∅ . [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00454-025-00806-6
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      – Code: eng
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      – SubjectFull: Topological spaces
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      – TitleFull: Short Proofs of Tverberg-Type Theorems for Cell Complexes.
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              Text: Jul2026
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